Fricke, Mathis ; Bothe, Dieter (2020)
Boundary conditions for dynamic wetting - A mathematical analysis.
In: The European Physical Journal Special Topics, 229 (10)
doi: 10.1140/epjst/e2020-900249-7
Article, Bibliographie
This is the latest version of this item.
Abstract
The moving contact line paradox discussed in the famous paper by Huh and Scriven has lead to an extensive scientific discussion about singularities in continuum mechanical models of dynamic wetting in the framework of the two-phase Navier–Stokes equations. Since the no-slip condition introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in [A.V. Lukyanov, T. Pryer, Langmuir 33, 8582 (2017)] aims for regular solutions through modified boundary conditions. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the boundary conditions have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model of Lukyanov and Pryer. It is found that solutions may still be singular for the latter model.
| Item Type: | Article |
|---|---|
| Erschienen: | 2020 |
| Creators: | Fricke, Mathis ; Bothe, Dieter |
| Type of entry: | Bibliographie |
| Title: | Boundary conditions for dynamic wetting - A mathematical analysis |
| Language: | English |
| Date: | 14 September 2020 |
| Publisher: | Springer |
| Journal or Publication Title: | The European Physical Journal Special Topics |
| Volume of the journal: | 229 |
| Issue Number: | 10 |
| DOI: | 10.1140/epjst/e2020-900249-7 |
| URL / URN: | https://link.springer.com/article/10.1140%2Fepjst%2Fe2020-90... |
| Corresponding Links: | |
| Abstract: | The moving contact line paradox discussed in the famous paper by Huh and Scriven has lead to an extensive scientific discussion about singularities in continuum mechanical models of dynamic wetting in the framework of the two-phase Navier–Stokes equations. Since the no-slip condition introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in [A.V. Lukyanov, T. Pryer, Langmuir 33, 8582 (2017)] aims for regular solutions through modified boundary conditions. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the boundary conditions have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model of Lukyanov and Pryer. It is found that solutions may still be singular for the latter model. |
| Uncontrolled Keywords: | Condensed Matter Physics, Materials Science, general, Atomic, Molecular, Optical and Plasma Physics, Physics, general, Measurement Science and Instrumentation, Classical and Continuum Physics |
| Additional Information: | Erstveröffentlichung; Part of collection: Challenges in Nanoscale Physics of Wetting Phenomena |
| Divisions: | DFG-Collaborative Research Centres (incl. Transregio) DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting Processes DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting Processes > Research Area B: Modeling and Simulation DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting Processes > Research Area B: Modeling and Simulation > B01: Modelling and VOF based Simulation of the Multiphysics of Irreversible Thermodynamic Transfer Processes at Dynamic Contact Lines Profile Areas Profile Areas > Thermo-Fluids & Interfaces 04 Department of Mathematics 04 Department of Mathematics > Analysis 04 Department of Mathematics > Analysis > Mathematical Modeling and Analysis 04 Department of Mathematics > Mathematical Modelling and Analysis |
| Date Deposited: | 05 Oct 2020 06:36 |
| Last Modified: | 02 May 2024 11:46 |
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Boundary conditions for dynamic wetting - A mathematical analysis. (deposited 26 Apr 2024 12:50)
- Boundary conditions for dynamic wetting - A mathematical analysis. (deposited 05 Oct 2020 06:36) [Currently Displayed]
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